The Transverality Theorem in Differentiable Topology by Guillemin and Pollack

Question

In Chapter 2, Section 3 of the book, most of the theorems requires the codomain $Y$ to be a manifold without the boundary and the submanifold $Z$ to be boundaryless as well. But I don't see why the boundaryless conditions of $Y$ and $Z$ are important. For example, the Transversality Theorem stated as the following:
Suppose that $F: X\times S\rightarrow Y$ is a smooth map of manifolds, where only $X$ has boundary, and let $Z$ be any boundaryless submanifolds of $Y$. If both $F$ and $\partial F$ are transversal to $Z$, then for almost every $s\in S$, both $f_s$ and $\partial f_s$ are transversal to $Z$.
I tried to construct some counterexample where either $Z$ or $Y$ to be a manifold with boundary, but I have no idea about how to construct such counterexample. Could someone give me some concrete example where the theorem fails when $Z$ or $Y$ has boundary? Thank you in advance.